Calculated structural properties of ${\mathrm{CrSi}}_2$, ${\mathrm{MoSi}}_2$, and ${\mathrm{WSi}}_2$

The linear augmented-plane-wave method has been applied to calculate the valence-electron contribution to the total energy of the hexagonal (C40) and tetragonal (C${11}_{\mathit{b}}$) phases of the group-VI transition-metal disilicides ${\mathrm{CrSi}}_2$, ${\mathrm{MoSi}}_2$, and ${\mathrm{WSi}}_2$ in the local-density approximation (LDA). In agreement with experiment, the results show that the tetragonal C${11}_{\mathit{b}}$ phase is the lower-energy structure for both ${\mathrm{MoSi}}_2$ and ${\mathrm{WSi}}_2$ (by 0.11 and 0.22 eV/formula unit, respectively). However, the LDA fails to replicate the observed switch to the stable hexagonal C40 phase in ${\mathrm{CrSi}}_2$, leaving a reduced but positive C40-C${11}_{\mathit{b}}$ structural-energy difference of 0.05 eV/formula unit. The calculated lattice parameters for the observed stable phases are in excellent agreement (∼0.01–0.03 Å) with measured values. Somewhat large discrepancies (∼0.1–0.3 Å) are found for the c lattice parameters of the metastable hexagonal ${\mathrm{MoSi}}_2$ and ${\mathrm{WSi}}_2$ compounds.